CPT-symmetry and the nature of time

Our follow-up to last summer’s PRL outlining a quantum resource theory for CPT-symmetry has hit the arXiv and been accepted for publication (without mods!) in PRA. We’ve got some further generalizations we’re starting to work on, but one of the things this work has crystallized in both my mind and many other people’s minds is that true “time-reversal” is really CPT-reversal. Nevertheless, there are still some pesky questions about time that persist, despite Ken Wharton’s argument that there’s really no funny business going on at all. Ken has tried to convince me to buy into the block universe explanation. I’m still not entirely sold on the idea, but I have come to believe that the problem of the nature of time as an “isolated” problem is less important than the relative nature time to space. In other words, I think the more important question that needs to be addressed is, why does the metric tensor that describes the universe have at least one negative eigenvalue, i.e. why is the sign of the time component always opposite to the sign of the spatial components in the metric?

Ken might answer that this is an artifact of our perception. For example, I might say that “normal” geometry, i.e. the Euclidean geometry of everyday life, doesn’t exhibit this feature. Ken might counter that that’s just a result of the fact that we perceive one of the four dimensions differently even though they’re all really the same. But that still leaves the question as to why we perceive that one dimension differently. It clearly is independent of the human mind since other species “perceive” time and time does appear to have some kind of preferred direction while space does not. Either way, the fact of the matter is that the metric tensor that describes the universe that we observe and measure has a negative eigenvalue, regardless of whether the space is flat or curved. We can’t magically force the metric to have only positive eigenvalues. Science is about describing what we can reliably measure with a healthy dose of Occam’s Razor thrown in for good measure. The simplest description of the universe’s geometry that matches experiment forces the presence of at least one negative eigenvalue in the metric tensor. Why? That’s the question that needs to be answered.

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2 Responses to “CPT-symmetry and the nature of time”

  1. Ken Wharton Says:

    Hi Ian,

    Just to clarify what I “might” say… 🙂

    I would not say that the metric signature is due to our perception; this is a real fact about our universe. But time and space are both dimensions that must be viewed in tandem rather than separately; questions should be asked about spacetime, not about time vs. space. I agree with you that one very important question is why spacetime has the metric signature that it does. (And I don’t have the faintest clue about the answer.)

    But the crucial similarity about all of the dimensions in our universe (no matter how you slice spacetime) is that NONE of them have a special “direction” built into the dimension itself. This is easiest to see if you think of spacetime all together, but hard to see if you just think about our typical experiences. (Yes, there may be boundary constraints that break local symmetries, but space doesn’t have an inherent “direction”, even on a hillside; time doesn’t have an inherent “direction”, even in a universe with a low-entropy big bang.) After all, isn’t this what CPT tells us is true?

    • quantummoxie Says:

      I hope you will forgive me putting words in your mouth (it’s better than putting words on your Scrabble board 😡 ). I absolutely agree that spacetime needs to be considered as a whole, otherwise it makes no sense. But that is precisely my point. A negative eigenvalue for the metric is meaningless without the knowledge that all the others are positive. The point is that the sign of one dimension is different from the sign of the other dimensions. Whether or not that implies a preferred direction for that one rogue dimension is a matter for debate. What is crucial, though, is that there’s something funky about that one dimension when compared to the others. That’s the important question to be answered.

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